Finite Group Databasebeta

← #25063156

Subgroups — #25063156

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3C2×C4⋊C8×D43C211yesmaximal, characteristic, complemented
4#19133009C211yesmaximal, characteristic, complemented
5#19133008C211yesmaximal, characteristic, complemented
6#19133006C211yesmaximal, characteristic, complemented
7#19132996C212yesmaximal, complemented
8#19132992C212yesmaximal, complemented
9#19132981C212yesmaximal, complemented
10#19132979C212yesmaximal, complemented
11C43×#1483C211yesmaximal, characteristic, complemented
12C22×C8×D43—21no—
13#14583455C411yescharacteristic
14#14583453C2211yescharacteristic
15#14583451C411yescharacteristic
16#14583448C411yescharacteristic
17#14583446C2211yescharacteristic
18#14583444C411yescharacteristic
19#14583434C411yescharacteristic
20#14583433C2211yescharacteristic
21#14583432—21no—
22#14583432—21no—
23#14583428C411yescharacteristic
24#14583427—21no—
25#14583426—21no—
26#14583412C411yescharacteristic
27#14583409C411yescharacteristic
28#14583408—21no—
29#14583407—21no—
30C4×#10621902C2211yescharacteristic
31#14583367—21no—
32C4×#10621900—21no—
33C4×#10621900C2211yescharacteristic
34C2×C42×D43C2211yescharacteristic
35#14582954—21no—
36#14582954—21no—
37#14582950C2212yes—
38#14582950C2212yes—
39#14582922—21no—
40C2×C4⋊(C43⋊C8)C2211yescharacteristic
41C2×Dic43⋊C8—21no—
42C4⋊C8×D43—21no—
43C4⋊C8×D43—21no—
44C4⋊C8×D43C2212yes—
45C4⋊C8×D43C2212yes—
46#14582862—21no—
47C4×#10621877C2211yescharacteristic
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C43×#529C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C4×M16×C43C2211yescharacteristic
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×#10621902C2×C411yescharacteristic
60C2×#10621898—21no—
61C2×#10621900—21no—
62C2×#10621900C2×C411yescharacteristic
63C22×C4×D43C2×C411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C2×#10621877—21no—
67C22×C43⋊C8—21no—
68C2×C8×D43—22no—
69C2×C8×D43—22no—
70C2×C8×D43—44no—
71#13063324C2×C411yescharacteristic
72#13063324C2×C411yescharacteristic
73#13063323C2×C411yescharacteristic
74#13063321C2×C411yescharacteristic
75#13063320—21no—
76#13063319—21no—
77#13063318—21no—
78#13063317C2×C411yescharacteristic
79#13063315—21no—
80#13063315—21no—
81#13063313C2×C411yescharacteristic
82#13063311—21no—
83#13063311—21no—
84#13063310—21no—
85#13063310—21no—
86#13063308—21no—
87#13063307—21no—
88#13063307—21no—
89#13063305C2×C411yescharacteristic
90#13063304C2×C411yescharacteristic
91#13063303—21no—
92#13063303—21no—
93#13063303—21no—
94#13063302—21no—
95#13063301C2×C411yescharacteristic
96#13063300C2×C411yescharacteristic
97#13063299C2×C411yescharacteristic
98#13063298—21no—
99#13063298—21no—
100#13063298—21no—
101#13063297—21no—
102#13063296C2×C411yescharacteristic
103#13063295—21no—
104#13063293—21no—
105Q8×Dic43C2×C411yescharacteristic
106C4×Dic86—21no—
107C4×Dic86C2311yescharacteristic
108#13063290—21no—
109#13063290—21no—
110#13063290—21no—
111#13063290C2×C411yescharacteristic
112C4×D172—21no—
113C4×D172C2311yescharacteristic
114D4×Dic43—21no—
115D4×Dic43C2×C411yescharacteristic
116#13063287—21no—
117#13063287—21no—
118#13063287—21no—
119#13063287C2×C411yescharacteristic
120C4×C22⋊D43—21no—
121C4×C22⋊D43—21no—
122C4×C22⋊D43—21no—
123(C22⋊D43)⋊C4—21no—
124(C22⋊D43)⋊C4—21no—
125(C22⋊D43)⋊C4—21no—
126(C22⋊D43)⋊C4—21no—
127(C22⋊D43)⋊C4—21no—
128(C22⋊D43)⋊C4—21no—
129(C22⋊D43)⋊C4—21no—
130#13063283—21no—
131#13063283—21no—
132#13063283C2×C411yescharacteristic
133#13063283C2×C411yescharacteristic
134#13063282—21no—
135#13063282—21no—
136#13063281—21no—
137#13063281—21no—
138#13063281—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43C2×C411yescharacteristic
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C42×D43—21no—
144C42×D43C2×C411yescharacteristic
145C42×D43C2×C411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43D411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43C2311yescharacteristic
151C42×D43C2311yescharacteristic
152C4⋊(C43⋊C8)—21no—
153C4⋊(C43⋊C8)C2312yes—
154Dic43⋊C8—22no—
155Dic43⋊C8—22no—
156Dic43⋊C8—22no—
157Dic43⋊C8—22no—
158(C2×D43)⋊C8—22no—
159(C2×D43)⋊C8—22no—
160#13063236—21no—
161C4×C43⋊C8C2312yes—
162C2×M16×C43—21no—
163C22×C8×C43—21no—
164#126×C43—21no—
165#125×C43C2×C411yescharacteristic
166#124×C43C2×C411yescharacteristic
167#123×C43—21no—
168C22⋊Q8×C43C2×C411yescharacteristic
169#121×C43C2×C411yescharacteristic
170C4×Q8×C43C2311yescharacteristic
171C4×D4×C43—21no—
172C4×D4×C43C2311yescharacteristic
173#117×C43—21no—
174C2×C42×C43C2311yescharacteristic
175C4⋊C8×C43—21no—
176C4⋊C8×C43C2312yes—
177#97×C43—21no—
178C4×C8×C43C2312yes—
179C23×D43C22⋊C411yescharacteristic
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43C22×C411yescharacteristic
183C22×C4×C43—21no—
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43C22⋊C411yescharacteristic
195C22×Dic43C22⋊C411yescharacteristic
196C22×Dic43C22⋊C411yescharacteristic
197#10621902—24no—
198#10621900—24no—
199#10621900—44no—
200#10621898—42no—
201#10621898—42no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172C22×C411yescharacteristic
205C2×C4×D43—24no—
206C2×C4×D43—22no—
207C2×C4×D43—22no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—42no—
212C2×C4×D43C22⋊C411yescharacteristic
213C2×C4×D43C22⋊C411yescharacteristic
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22⋊C411yescharacteristic
216C2×C4×D43C22⋊C411yescharacteristic
217C2×C4×D43C22⋊C411yescharacteristic
218C2×C4×D43C22×C411yescharacteristic
219C2×C4×D43C22×C411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×C4×D43C2×D411yescharacteristic
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86C22×C411yescharacteristic
227M16×C43—42no—
228C2×C8×C43—22no—
229C2×C8×C43—22no—
230C2×C8×C43—42no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C22×C411yescharacteristic
236C4⋊C4×C43C22×C411yescharacteristic
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C22⋊C4×C43—21no—
240C22⋊C4×C43—21no—
241C22⋊C4×C43—21no—
242C42×C43—21no—
243C42×C43C22×C411yescharacteristic
244C42×C43C2×D411yescharacteristic
245C42×C43C2×D411yescharacteristic
246C42×C43C2411yescharacteristic
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250(C2×D43)⋊C4—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259(C2×D43)⋊C4—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C22×C411yescharacteristic
263C4⋊Dic43C22×C411yescharacteristic
264Dic43⋊C4—21no—
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274C4×Dic43—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22×C411yescharacteristic
286C4×Dic43C22×C411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290C4×Dic43C2×D411yescharacteristic
291#10621877—42no—
292C2×C43⋊C8—22no—
293C2×C43⋊C8—22no—
294C2×C43⋊C8—42no—
295C8×D43—44no—
296C8×D43—44no—
297C23×C43—21no—
298C23×C43C2×C22⋊C411yescharacteristic
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—21no—
303C22×D43C2×C22⋊C411yescharacteristic
304C22×D43C2×C22⋊C411yescharacteristic
305Q8×C43—22no—
306D4×C43—22no—
307D4×C43—42no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43C2×C22⋊C411yescharacteristic
318C2×C4×C43C2×C22⋊C411yescharacteristic
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C23×C411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C22×D411yescharacteristic
323C22⋊D43—42no—
324C22⋊D43—42no—
325C22⋊D43—42no—
326C22⋊D43—42no—
327C22⋊D43—42no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342D172—22no—
343D172—42no—
344D172—42no—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—21no—
349C4×D43—21no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—41no—
353C4×D43—41no—
354C4×D43—41no—
355C4×D43—41no—
356C4×D43—42no—
357C4×D43—41no—
358C4×D43—41no—
359C4×D43—42no—
360C4×D43#13114yes—
361C4×D43AGL(1,ℤ/8)12yes—
362C4×D43#13712yes—
363Dic86—22no—
364Dic86—42no—
365Dic86—42no—
366C8×C43—42no—
367C8×C43—42no—
368C43⋊C8—42no—
369C43⋊C8—42no—
370#17466—431nomaximal, Sylow
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43#42112yes—
377C22×C43C22×C22⋊C411yescharacteristic
378C2×D43—28no—
379C2×D43—21no—
380C2×D43—21no—
381C2×D43—21no—
382C2×D43—21no—
383C2×D43—41no—
384C2×D43—41no—
385C2×D43—41no—
386C2×D43#40812yes—
387C2×D43#41712yes—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—41no—
393C4×C43—41no—
394C4×C43—41no—
395C4×C43C2×#13112yes—
396C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
397C4×C43C2×#13711yescharacteristic
398Dic43—21no—
399Dic43—21no—
400Dic43—21no—
401Dic43—21no—
402Dic43—41no—
403Dic43—41no—
404Dic43—41no—
405Dic43#40812yes—
406Dic43#41712yes—
407#3444—431no—
408#2920—431no—
409C22×C4⋊C8—431no—
410#1483—431no—
411#1483—431no—
412#1483—431no—
413#1483D4311yescharacteristic, complemented
414#1481—432no—
415#1480—432no—
416#1477—432no—
417#1477—432no—
418C2×C43—22no—
419C2×C43—81no—
420C2×C43C2×#40811yescharacteristic
421C2×C43C2×#41711yescharacteristic
422C2×C43C2×#42111yescharacteristic
423D43—22no—
424D43—22no—
425D43—81no—
426C23×C8—861no—
427#533—431no—
428#533—431no—
429#533—431no—
430#532—431no—
431#532—431no—
432#532—431no—
433#529—431no—
434#529—431no—
435#529—431no—
436#529—861no—
437#529—861no—
438#529—861no—
439#529—861no—
440#529C2×D4311yescharacteristic
441#525—431no—
442#525—431no—
443#525—861no—
444#525—861no—
445C4×#41—431no—
446C4×#41—431no—
447C4×#41—861no—
448C4×#41—861no—
449C22×C42—431no—
450#432—861no—
451#432—861no—
452#431—432no—
453#431—432no—
454#423—861no—
455C2×C4⋊C8—431no—
456C2×C4⋊C8—432no—
457C2×C4⋊C8—432no—
458C2×C4⋊C8—861no—
459C2×C4⋊C8—861no—
460C2×C4⋊C8—861no—
461C2×C4⋊C8C2×D4311yescharacteristic
462#407—861no—
463C4×M16—431no—
464C4×M16C2×D4311yescharacteristic
465Q8⋊C8—432no—
466Q8⋊C8—432no—
467Q8⋊C8—432no—
468Q8⋊C8C2×D4312yescomplemented
469D4⋊C8—432no—
470D4⋊C8—432no—
471D4⋊C8—432no—
472D4⋊C8C2×D4312yescomplemented
473C43#1746611yescharacteristic, complemented, Sylow
474C2×#41—431no—
475C2×#41—431no—
476C2×#41—861no—
477C2×#41—861no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—431no—
481C2×M16—21no—
482C2×M16—861no—
483C22×C8—21no—
484C22×C8—862no—
485C22×C8—862no—
486C22×C8—861no—
487C22×C8—1724no—
488C4⋊Q8—431no—
489C4⋊Q8—431no—
490C4⋊Q8—431no—
491#127—431no—
492#126—21no—
493#126—861no—
494#126—861no—
495#126—861no—
496#125—431no—
497#125—861no—
498#125—861no—
499#125C4×D4311yescharacteristic
500#124—431no—
501#124—861no—
502#124—861no—
503#124C4×D4311yescharacteristic
504#123—21no—
505#123—861no—
506#123—861no—
507#123—861no—
508#123—861no—
509#123—861no—
510C22⋊Q8—431no—
511C22⋊Q8—431no—
512C22⋊Q8—431no—
513C22⋊Q8—861no—
514C22⋊Q8—861no—
515C22⋊Q8—861no—
516C22⋊Q8—861no—
517C22⋊Q8C4×D4311yescharacteristic
518#121—431no—
519#121—431no—
520#121—431no—
521#121—861no—
522#121—861no—
523#121—861no—
524#121—861no—
525#121C4×D4311yescharacteristic
526#120—861no—
527#120—861no—
528C4×Q8—431no—
529C4×Q8—431no—
530C4×Q8—431no—
531C4×Q8—861no—
532C4×Q8—861no—
533C4×Q8—861no—
534C4×Q8—861no—
535C4×Q8C22×D4311yescharacteristic
536C4×D4—21no—
537C4×D4—431no—
538C4×D4—431no—
539C4×D4—431no—
540C4×D4—861no—
541C4×D4—861no—
542C4×D4—861no—
543C4×D4—861no—
544C4×D4—861no—
545C4×D4—861no—
546C4×D4—861no—
547C4×D4—861no—
548C4×D4—861no—
549C4×D4—861no—
550C4×D4—861no—
551C4×D4—861no—
552C4×D4—861no—
553C4×D4—861no—
554C4×D4—861no—
555C4×D4C22×D4311yescharacteristic
556#117—21no—
557#117—431no—
558#117—431no—
559#117—861no—
560#117—861no—
561#117—861no—
562#117—861no—
563#117—861no—
564#117—861no—
565#117—861no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—431no—
574C2×C42—431no—
575C2×C42—431no—
576C2×C42—431no—
577C2×C42—861no—
578C2×C42—861no—
579C2×C42C22×D4311yescharacteristic
580C4⋊C8—21no—
581C4⋊C8—432no—
582C4⋊C8—862no—
583C4⋊C8—862no—
584C4⋊C8—862no—
585C4⋊C8—862no—
586C4⋊C8—861no—
587C4⋊C8C22×D4312yes—
588C22⋊C8—862no—
589C22⋊C8—862no—
590#97—21no—
591#97—861no—
592C4×C8—432no—
593C4×C8C22×D4312yes—
594C24—431no—
595#41—864no—
596#41—864no—
597#41—1722no—
598#41—1722no—
599#41—1724no—
600C2×Q8—431no—
601C2×Q8—861no—
602C2×Q8—861no—
603C2×Q8C2×C4×D4311yescharacteristic
604C2×D4—21no—
605C2×D4—431no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4C2×C4×D4311yescharacteristic
614C22×C4—21no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—862no—
631C22×C4—864no—
632C22×C4—862no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—1722no—
639C22×C4C2×C4×D4311yescharacteristic
640C22×C4D4×D4311yescharacteristic
641C22×C4D4×D4311yescharacteristic
642M16—42no—
643M16—1722no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—42no—
647C2×C8—862no—
648C2×C8—862no—
649C2×C8—1724no—
650C2×C8—1724no—
651C2×C8—1722no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—431no—
657C4⋊C4—431no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4C2×C4×D4311yescharacteristic
671C4⋊C4C2×C4×D4311yescharacteristic
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
681C22⋊C4—861no—
682C22⋊C4—861no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C22⋊C4—861no—
687C22⋊C4—861no—
688C22⋊C4—861no—
689C22⋊C4—861no—
690C42—21no—
691C42—431no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—431no—
701C42—431no—
702C42—431no—
703C42—861no—
704C42—861no—
705C42—861no—
706C42—861no—
707C42—861no—
708C42C2×C4×D4311yescharacteristic
709C42D4×D4311yescharacteristic
710C42D4×D4311yescharacteristic
711C42C23×D4311yescharacteristic
712C23—21no—
713C23—431no—
714C23—431no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—861no—
719C23C22⋊C4×D4311yescharacteristic
720Q8—22no—
721Q8—862no—
722Q8—1722no—
723Q8—1722no—
724D4—22no—
725D4—42no—
726D4—862no—
727D4—1722no—
728D4—1722no—
729D4—1722no—
730D4—1722no—
731D4—1722no—
732D4—1722no—
733D4—1722no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—431no—
744C2×C4—431no—
745C2×C4—434no—
746C2×C4—432no—
747C2×C4—432no—
748C2×C4—431no—
749C2×C4—431no—
750C2×C4—431no—
751C2×C4—431no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—861no—
761C2×C4—861no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1721no—
768C2×C4—1721no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4—1721no—
774C2×C4—1721no—
775C2×C4C22⋊C4×D4311yescharacteristic
776C2×C4C22⋊C4×D4311yescharacteristic
777C2×C4C22⋊C4×D4311yescharacteristic
778C2×C4C22×C4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C2×C4C2×D4×D4311yescharacteristic
781C8—42no—
782C8—42no—
783C8—1722no—
784C8—1722no—
785C22—21no—
786C22—21no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—432no—
791C22—432no—
792C22—868no—
793C22—861no—
794C22—861no—
795C22—861no—
796C22—861no—
797C22—1721no—
798C22—1721no—
799C22—1721no—
800C22#1458291412yes—
801C22C2×C22⋊C4×D4311yescharacteristic
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—432no—
810C4—432no—
811C4—861no—
812C4—861no—
813C4—861no—
814C4—861no—
815C4—1721no—
816C4—1721no—
817C4—1721no—
818C4#131×D4312yes—
819C4AGL(1,ℤ/8)×D4311yescharacteristic
820C4#137×D4311yescharacteristic
821C2—22no—
822C2—81no—
823C2—862no—
824C2—862no—
825C2—3441no—
826C2#408×D4311yescharacteristic
827C2#417×D4311yescharacteristic
828C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1483C2
socleC22×C43C22×C22⋊C4
prime radical#19147889C2
cosocleC42×C43C24
hypercenter#1483D43
hypocenterC43#17466
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19143226C2semidirect
3. C2×C4⋊C8×D43C2semidirect
4. #19133009C2semidirect
5. #19133008C2semidirect
6. #19133006C2semidirect
7. #19132996C2semidirect
8. #19132992C2semidirect
9. #19132981C2semidirect
10. #19132979C2semidirect
11. C43×#1483C2semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
413. #1483D43semidirect
468. Q8⋊C8C2×D43semidirect
472. D4⋊C8C2×D43semidirect
473. C43#17466semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191478892
#191432262
C2×C4⋊C8×D432
#191330092
#191330082
#191330062
#191329962
#191329922
#191329812
#191329792
C43×#14832
#1746643